随机过程的最优控制、稳定性理论及其应用研究

项目名称： 随机过程的最优控制、稳定性理论及其应用研究

项目编号： No.10801056

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 生物科学

项目作者： 朱全新

作者单位： 宁波大学

项目金额： 17万元

中文摘要： 三年来,我们对这个国际重要课题进行了系统、深入的研究,并取得了如下成果：(1)率先研究了一般状态空间连续时间马氏决策过程中的期望平均、Bias、Overtaking、强n折扣、平均样本轨道和平均方差等准则下的最优控制问题及有效算法；证明了最优策略的存在性,首次获得平均样本轨道和平均方差最优策略不一定是标准策略的新结果，建立了Bias最优方程，得到了Bias和Overtaking最优性的等价关系，研究了强n折扣与期望平均、Bias准则之间的关系，并最终解决了期望平均准则的策略迭代算法。(2)提出了多类新的复杂随机系统模型,并深入研究了它们的渐进稳定、指数稳定、振动性和非振动性；研究表明, 这些新模型具有很大的一般性,时变时滞、混合时滞、参数不确定、中立型、非线性、噪音和脉冲等因素对系统的稳定性有重要影响。（3）研究了金融数学的期权价格、生物数学中的捕食和复杂网络的同步等重要应用问题。成果发展了许多新的理论和方法,并解决了相关开问题。发表论文55篇，其中SCI占38篇，远远超出了原计划10篇SCI的预期目标。特别，论文得到大量广泛引用与好评,部分结果已获得国家、省、市等多项科研成果奖励。

中文关键词： 随机过程；最优控制; 稳定性理论; 随机神经网络; 连续时间马氏决策过程

英文摘要： We have been overall and deeply studying the project that is an important and international research topic for three years and obtained the following interesting results: (1) We studied initiately optimal control problems and effective algorithms of some criteria, such as expected average, Bias, Overtaking, strong discounts, average sample path and average variance, in continuous-time Markov decision process with a general state space; We proved the existence of the optimal policy, and firstly obtained an average sample path (average variance) optimal policy may not be canonical, the Bias optimal equation, the equivalent relation between Bias and Overtaking optimality, the relation among strong n-discount, expected average and Bias, as well as the policy iteration algorithm of expected average. (2) We introduced many new types of more complex stochastic systems, and further studied their asymptotic stability, exponential stability, vibration and non-oscillation; our research shows that these systems are quite general and a lot of factors such as time-varying delays, mixed delays, parameter uncertainties, neutral, nonlinear, noises and impulses have an important effect of the stability. (3) We studied some important application issues such as the option price of financial mathematics, predation of biological mathematics and synchronization of complex networks. Many new theories and methods have been developed and some open issues have been studied in our results. We have published 55 papers, where SCI papers are 38. So our achievements are far beyond the original plan 10 targets of SCI. In particular, our results have gotten a lot of widely quoted and the high praise, and some results have obtained the national、provincial、 municipal and many scientific research awards.

英文关键词： Stochastic process; Optimal control; Stability theory; Stochastic neural network; Continuous-time Markov decision process